Things like mailing addresses and address changes are only ONE very small part of establishing residency. If his stuff is elsewhere, he's been residing elsewhere, or the really obvious thing like paying rent to someone else has occurred, that's MORE than enough to establish that he HAS established residency elsewhere. Your parents have NO legal obligation to re-admit him to their home.
And if he decides to push it, remind him that HE is legally obligated to change his address on things like his driver's license - usually within 10 days in most states - or else HE is looking at violations, tickets, etc. His failure to obey such laws doesn't create liability for your parents, but can result in some nifty fines for HIM.

